Exploiting Self-Similarity in Geometry for Voxel Based Solid Modeling

[+] Author and Article Information
Tushar Udeshi

Zyvex Corporation, 1321 N Plano Road, Richardson, TX 75081e-mail: tudeshi@zyvex.com

Eric Parker

Inmetrix Corporation, 17 Meadowlake Drive, Heath, TX 75032e-mail: eric@inmetrix.com

J. Comput. Inf. Sci. Eng 4(1), 49-55 (Mar 23, 2004) (7 pages) doi:10.1115/1.1641187 History: Received July 01, 2003; Revised October 01, 2003; Online March 23, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Kolb, A., and John, L., 2001, “Volumetric Model Repair for Virtual Reality Applications,” Proceedings of Eurographics, Short paper presentation, Chalmers. A. and Rhyne. M., T, eds., Manchester, UK.
Wood, Z., Hoppe, H., Desburn, M., and Schroder P., 2002, “Isosurface Topology Simplification,” Microsoft Technical Report MSR-TR-2002-28, Seattle, WA.
Frisken, F., and Perry, R., 2001, “Kizamu: A System for Sculpting Digital Characters,” Proceedings of the 28th annual conference on Computer graphics and interactive techniques, Pocock L., ed., ACM Press, pp. 47–56.
Kaufman, A., and Shimony, E., 1986, “3D Scan-Conversion Algorithms for Voxel-Based Graphics,” Proceedings of 1986 Workshop on Interactive 3D Graphics, Chapel Hill, NC, pp. 45–75.
Srámek,  M., and Kaufman,  A., 2000, “Alias-Free Voxelization of Geometric Objects,” IEEE Trans. Vis. Comput. Graph., 3(6), pp. 236–252.
Udeshi, T., 2003, “Tetrahedral Mesh Generation from Segmented Voxel Data,” Proceedings of the 12th International Meshing Roundtable, Santa Fe, NM, pp. 425–436.
Kaufman,  A., Cohen,  D., and Yagel,  R., 1993, “Volume Graphics,” IEEE Trans. Comput., 26(7), pp. 51–64.
Samet, H., 1990, The Design and Analysis of Spatial Data Structures, Addison-Wesley, Reading.
Noh, W., and Woodward, P., 1976, “Simple Line Interface Calculation,” Lecture Notes in Physics, 59 , Springer-Verlag, pp. 330–340.
Hanan,  S., 1985, “Data Structures for Quadtree Approximation and Compression,” Commun. ACM, 28(9), pp. 973–993.
Gosper,  R., 1984, “Exploiting Regularities in Large Cellular Spaces,” Physica D, 10, pp. 75–80.
Webber,  R. E., and Dillencourt,  M. B., 1989, “Compressing Quadtrees via Common Subtree Merging,” Pattern Recogn. Lett., 9(3), pp. 193–2000.
Parker, E., and Udeshi, T., 2003, “Exploiting Self-Similarity in Voxel-Based Solid Modeling,” 8th ACM Symposium on Solid Modeling and Applications, Gershin, E. and Shapiro, V., eds., Seattle, WA, pp. 157–166.
Serra, J., 1984, Image Analysis and Mathematical Morphology, Academic Press, New York, NY.
Yarberry, V., 2002, “Meeting the MEMS ‘Design-to-Analysis’ Challenge: The SUMMIT® V Design Tool Environment,” Proceedings of ASME International Mechanical Engineering Congress & Exposition, Micro-Electro-Mechanical Systems (MEMS), New Orleans, LA, pp. 547–553.
Tan, Z., Furmanczyk, M., Turowski, M., and Przekwas, A. J., 2001, “CFD-Micromesh: A Fast Geometrical Modeling and Mesh Generation Tool for 3D Microsystem Simulations,” Technical Proceedings of the 2000 International Conference on Modeling and Simulation of Microsystems, San Diego, CA, pp. 712–715.
Lorensen, W., and Cline, H., 1987, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics,” Proceedings of the 14th annual conference on Computer graphics and interactive techniques, Stone, M. C. ed., ACM Press, pp. 163–169.
Schroeder, W., Zarge, J., and Lorensen, W., 1992, “Decimation of Triangle Meshes,” Proceedings of the 19th annual conference on Computer graphics and interactive techniques, Thomas, J., ed., ACM Press, pp. 65–70.
Tao, J., Losasso, F., Schaefer, S., and Warren J., 2002, “Dual Contouring of Hermite Data,” Proceedings of the 29th annual conference on Computer graphics and interactive techniques, Appolloni, T., ed., ACM Press, pp. 339–346.
Rusinkiewicz, S. and Levoy, M., 2000, “QSplat: A Multiresolution Point Rendering System for Large Meshes,” Proceedings of the 2001 symposium on Interactive 3D graphics Computer Graphics, Hughes J.F., and Sequin, C. H., eds., ACM Press, pp. 353–358.
Aho, A., Hopcroft, J., and Ullman, J., 1983, Data Structures and Algorithms, Addison-Wesley, Reading.


Grahic Jump Location
Storage Savings for MEMS device 15640×11046×96 voxels. Array: 49,754,718,720 bytes. Adaptive Octree: 11,900,655,552 bytes. Shared Octree: 24,640,088 bytes. Savings w.r.t full octree: 99.95%.
Grahic Jump Location
Cross section of LPCVD along an edge. The green region shows the actual result. The red is the error introduced by doing a solid modeling offset. The percentage error along the edge is: 1−π/4/π/4=27.32%
Grahic Jump Location
Left: SEM image of a MUMPS device. Right: Geometry generated by MEMulator™. A leading MEMS CAD software package failed when given this input.
Grahic Jump Location
A MEMS device, modeled with 2856×4464×150 voxels. Isosurface extraction time (including squeezing) with results matching: 4.27 seconds. Without results matching on the same PC: 28.78 seconds.
Grahic Jump Location
Quarter of a die (0.5×0.5 cm) simulated and rendered at a quarter of a micron resolution.
Grahic Jump Location
A scenario where results matching should not be used. Component 3 is not connected with any of the lower neighbors.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In